Simplify (2x^2)^3 * x^4 Step by Step

Step by step

Question: simplify (2x²)³(x⁴).

(2x²)³(x⁴)

The power 3 outside the bracket means: the whole bracket, 3 times.

(2x²)³ = (2x²)(2x²)(2x²)

So we write the bracket out, times itself.

= ((2x²))((2x²))((2x²))(x⁴)

In times, the order does not matter.

So numbers go with numbers, and each letter goes with the same letter.

order does not matter: ab = ba

We put them in groups.

= (2 × 2 × 2)(x² x² x² x⁴)

So the rule is: same letter, times, add the powers.

2 plus 2 plus 2 plus 4 is 10.

2 + 2 + 2 + 4 = 10

x^a x^b = x^{a + b}

2 times 2 times 2 is 8.

So we get 8x¹⁰.

= 8x¹⁰

Let's look back.

First: write the power out.

Then: numbers with numbers.

Last: count the letters.

Answer

= 8x¹⁰